Two shuffleboard disks of equal mass, one orange and the other green, are involv

Question

Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at oi = 4.85 m/s as in Figure (a) shown below. After the collision, the orange disk moves in a direction that makes an angle of ? = 40.0° with the horizontal axis while the green disk makes an angle of = 50.0° with this axis as in figure (b). Determine the speed of each disk after the collision. (Note that ? + = 90.0°.)

Vf1=?
Vf2=?

Explanation / Answer

before collision:

orange moves horizontal v=4.85

after collision:

orange moves away with say, 'u' velocity, making 40 degrees with the horizontal and green moves away with say, 'v' velocity, making 50 degrees with the horizontal.

no momentum in the vertical direction, hence impulses are cancelled off

u = 0.766v/0.643

horizontal direction is the line of collision, hence momentum is conserved here

m(0) + m(4.85) = m(0.766u) + m(0.643v)

v/0.643 * [(0.643)^2 + (0.766)^2] = 4.85

v = 4.89 * 0.643 =3.118 m/s

u = 4.89 * 0.766 = 3.745 m/s.

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